# How to convert a ColorDistance from “CIE76” to “CIE2000”?

Consider, two unknown colors whose ColorDistance(Euclidean Distance (Default) in the CIE LAB color space) is 10 (say), where L ranges from 0 to 100, a from -128 to 127 and b from -128 to 127. Is it possible to find the corresponding ColorDistance with the DistanceFunction->"CIE2000"?

Edit 1:

Basically, I need to calculate the JND (Just Noticeable Difference) value for the DistanceFunction->"CIE2000". According to the CIE2000 documentation, the JND value is 1 (where L ranges from 0 to 100, a from -128 to 127 and b from -128 to 127). However, since in Mathematica L ranges from 0 to 1 while a and b typically range from -1 to 1, I don't know how to find the corresponding JND value in Mathematica.

• Knowing the distance between two points in one metric space doesn't tell you the distance in another metric space. I would be very surprised if two color spaces' metrics were isomorphic. – Searke Jul 26 '18 at 14:36
• Is there a reason you need to do this? Do you not have access to the original colors for some reason? At any rate, the formulas for the color distance can be found by searching online. The formulas are pretty complicated. – Searke Jul 26 '18 at 14:37
• @Searke Actually, I need the JND (just noticeable difference) threshold limit which is 5 (worst case) according to this (wisotop.de/assets/2017/DeltaE-%20Survey-2.pdf) [page 15, section 6.2] and I need the corresponding distance value for DistanceFunction->"CIE2000" – Majis Jul 26 '18 at 14:42

As @Searke pointed out in the comments, it is in general not possible to compute the distance according to one metric given the distance according to another one. A simple example that clearly demonstrates this is the following:

{a,b,c}=LABColor/@{{0,0,0},{1,0,0},{0,1,0}};

ColorDistance@@@{{a,b},{a,c}}
(* {1.,1.} *)

ColorDistance[##,DistanceFunction->"CIE2000"]&@@@{{a,b},{a,c}}
(* {1.,0.307876} *)


As you can see, both color pairs have distance 1 in the default metric but have completely different distances according to the CIE-2000 metric.